Download FALLING OBJECTS - NYU Tandon School of Engineering

FALLING OBJECTS
by
Edna T. Diolata
Brooklyn Technical High School
and
David Latman
Clara Barton High School For The Health Professions
INTRODUCTION
A simple experiment on falling bodies such as the one we have devised will touch on
many important lessons in a physics class- mass, weight, force of gravity, velocity,
terminal velocity, acceleration, aerodynamic drag, and Newton’s laws of motion. In a
technology class, this experiment will be helpful in a project where students design a
container for an egg that is to be dropped from a height of 20-30 feet without the egg
breaking.
Our experiment looks at external forces, namely, the force of gravity and air resistance or
aerodynamic drag. We want our students to analyze how the motion of falling objects is
affected by these forces as well as by such factors as mass, initial height, and crosssectional area.
BACKGROUND
When an object falls through air, it usually encounters some degree of air resistance. Air
resistance is the result of an object plowing through a layer of air and colliding with air
molecules. The greater the cross-sectional area of an object, the greater the amount of air
resistance it encounters since it collides with more air molecules. Furthermore, as an
object falls, it is being pulled downward by the force of gravity. At the start of the fall,
the force of gravity is an unbalanced force. This causes the object to gain speed or to
accelerate. As it accelerates, it encounters air resistance or aerodynamic drag. The
amount of air resistance depends upon the speed of the falling object. This can be
explained by Newton’s first and second laws and by the notion of terminal velocity.
According to Newton’s laws, an object will gain speed if the forces acting upon it are
unbalanced; and, the amount of acceleration is directly proportional to the net force
(unbalanced force) acting upon it. Falling objects initially accelerate because there is no
force large enough to balance the gravitational force. However, as an object gains speed,
it encounters more air resistance. It will continue to gain speed until the upward air
resistance force equals the downward force of gravity. When a falling object has a large
mass, it weighs more and will encounter a greater downward force of gravity. (Weight is
equal to the mass of the object times the gravitational acceleration, or W = mg). It will
have to accelerate for a longer period of time before there is enough upward air resistance
to balance the downward force of gravity.
Once the aerodynamic drag is exactly equal to the weight of the falling object, there is no
net external force acting on it anymore. Hence, it ceases to accelerate and the speed with
which it falls becomes constant. Once this happens, the falling object is said to have
reached terminal velocity.
LIST OF EQUIPMENT
To conduct our experiment, we needed a device that can accomplish these tasks:
1. Drop an object from a certain height
2. Provide air flow that can be regulated at various rates
3. Measure the time of the object’s fall and its speed at various times during the fall
Shown below are the various equipments that we used:
Standard Rotation Servo
Infrared Detector and
Infrared Light Emitting Diode
Ultrasonic Sensor (PING)
Board of Education and Basic Stamp2
Microcontroller
Solderless Breadboard
Power Supply
Jumper wires
Plexiglass
Resistors
Fan
THE COMPLETED DEVICE
SCHEMATIC DRAWING OF THE CIRCUITS
Top IR LED and IR Detector
Bottom IR LED and IR Detector
Standard Rotation Servo
PROGRAMMING CODE
' {$STAMP BS2}
' {$PBASIC 2.5}
'Falling Objects Experiment
'' -----I/O Definitions------------------------------------------------Ping
PIN 4
' -----Constants------------------------------------------------------Trigger
CON 5
' trigger pulse = 10 uS
Scale
CON $200
' raw x 2.00 = uS
RawToIn
CON 889
' 1 / 73.746 (with **)
RawToCm
CON 2257
' 1 / 29.034 (with **)
IsHigh
CON 1
' for PULSOUT
IsLow
CON 0
'--------------VARIABLES----------------------------------------------counter
VAR Word
IRtop
VAR Byte
IRbottom
VAR Byte
IRbottom2
VAR Byte
user
VAR Byte
time
VAR Byte
cm
VAR Word
rawDist
VAR Word
' raw measurement
totalTime
VAR Word
duty
VAR Byte
duration
VAR Byte
counter1
VAR Word
'-------------Main------------------------------------------------------Main:
LOW 3
PAUSE 20
Ultrasonic Sensor
PULSOUT 3, 500
PAUSE 20
PWM 2, duty, duration
DEBUG CLS
DEBUG "Select experiment:", CR
DEBUG "1: Shape and Size", CR
DEBUG "2: Mass", CR
DEBUG "3: Terminal Velocity", CR
DEBUGIN DEC user
IF user = 1 THEN GOSUB ShapeSize
IF user = 2 THEN GOSUB Mass
IF user = 3 THEN GOSUB TerminalVelocity
END
'-------------SUBROUTINES-----------------------------------------------Timer:
FOR counter = 1 TO 10
PULSOUT 3, 750
PAUSE 20
NEXT
DO
FREQOUT 1, 1, 38500
IRtop = IN0
LOOP UNTIL IRtop = 1
counter1 = 0
DEBUG CLS
DEBUG HOME, "Time | Distance", CR
DEBUG "(ms) | (cm)",CR
DO
counter1 = counter1 + 3 '10
FREQOUT 6, 1, 38500
IRbottom = IN2
FREQOUT 6, 1, 38500
IRbottom2 = IN5
'IRbottom2 = IN5
GOSUB sonar
cm = rawDist ** RawToCm
DEBUG DEC3 counter1, " | ", DEC3 cm, CR
PAUSE 7'70
LOOP UNTIL ( IRbottom = 1) OR (IRbottom2 = 1)
RETURN
'------------------ULTRASONIC------------------------------------------------------sonar:
Ping = IsLow
' make trigger 0-1-0
PULSOUT Ping, Trigger
' activate sensor
PULSIN Ping, IsHigh, rawDist
' measure echo pulse
rawDist = rawDist */ Scale
' convert to uS
rawDist = rawDist / 2
' remove return trip
RETURN
'------------------Shape and Size------------------------------------------------ShapeSize:
GOSUB Timer
DEBUG "To repeat procedure press 1 or 2 to go to main", CR
DEBUGIN DEC user
IF user = 1 THEN GOSUB ShapeSize
IF user = 2 THEN GOSUB Main
END
'------------------MASS---------------------------------------------------------Mass:
GOSUB Timer
DEBUG "To repeat procedure press 1 or 2 to go to main", CR
DEBUGIN DEC user
IF user = 1 THEN GOSUB Mass
IF user = 2 THEN GOSUB Main
END
'-----------------ThermalVelocity------------------------------------------------TerminalVelocity :
DEBUG CLS
DEBUG "Set the Speed of the fan", CR
DEBUG "Press 1 to Initiate", CR
DEBUGIN DEC user
IF user = 1 THEN GOSUB Timer
DEBUG "To repeat procedure press 1 or 2 to go to main", CR
DEBUGIN DEC user
IF user = 1 THEN GOSUB TerminalVelocity
IF user = 2 THEN GOSUB Main
END
EXPERIMENTAL PROCEDURE
A. Goals
1. To determine how objects of the same mass but different cross-sectional areas are
affected by air resistance (henceforth will be referred to as Experiment 1)
2. To determine how objects of the same cross-sectional areas but different masses are
affected by air resistance (henceforth will be referred to as Experiment 2)
3. To determine how air resistance and the mass and cross-sectional area of an object
affect terminal velocity (henceforth will be referred to as Experiment 3)
B. Procedure
For experiment 1, we have chosen three objects: a flat object with a wide cross-sectional
area, a box, and a cup. With the use of a massing scale, we made sure that they all have
the same mass. (An object’s mass is the amount of matter it contains.) We begin the
experiment by placing an object on the trapdoor at the top of the device. This trapdoor is
secured by a pin that is powered by a servomotor. The trapdoor opens, drops the object,
and a pair of IR LED and Detector sense it and send a pulse to the Basic Stamp, which in
turn sends a signal to the computer. The computer begins to mark the time of the object’s
descent in milliseconds. The fan at the bottom provides air flow, which is set at a constant
rate. When the object hits bottom, another pair of IR LED and IR detector sense the
object and again a signal is sent to the computer, which records the final time of the fall.
Attached to the platform at the bottom is an ultrasonic sensor (PING) that measures the
distance at each millisecond of the object’s fall. This allows us to track the speed of the
fall. The speed and time data is then copied onto a spreadsheet.
B. The same procedure used in Experiment 1 will be used in conducting Experiment 2. In
this experiment, the input variable is the difference in mass of three objects of the same
size and shape.
C. Experiment 3 involves dropping the same object but using four different rates of air
flow.
C. Results and Discussion
(Averages after three trials)
Experiment 1
Disk shape
Box
Cup
Experiment 2
Object1 (1.8 g)
Object2 (3.3 g)
Object3 (6.6 g)
Time of Fall in Milliseconds
With Air Flow
Without Air Flow
33
32
30
31
28
28
Time of Fall in Milliseconds
With Air Flow
Without Air Flow
94
46
65
40
35
33
Terminal Velocity in Milliseconds
Experiment 3
High Air Flow
Medium Air Flow
Low Air Flow
No Air Flow
Note: We were not able to conduct Experiment 3 due to limitations with the device.
From the results shown above, we derive the following conclusions:
• When there’s air flow, an object with greater surface or cross-sectional area fall
slower. This is because it encounters more air resistance, which slows it down.
•
•
•
•
•
When there’s no air flow, objects in general drop faster. This is because they
encounter less air resistance.
Objects with greater mass encountering air resistance fall faster. This is because
they are heavier and experience greater downward force of gravity.
When there’s no air resistance, mass has little impact on the speed of the fall.
The height of the device at 32 inches does not give us appreciable differences in
the results. The distance of the fall is too short and the air flow from the fan is not
fast or strong enough to counter the force of gravity. Our solution to this problem
was to use very light objects. However, the problem here is that they tend to
bounce around inside the container causing the sensors to give the wrong signals.
The design of the device needs to be revised in order to conduct Experiment 3.
How will this device be used in our classes? Our students will conduct their own
experiments following the aforementioned experimental procedure, create their own
tables and graphs of the results, extrapolate from these, and draw their own conclusions.
FUTURE WORKS
1. Conduct further experiments on the motion of falling bodies, such as:
• Objects of same mass, different cross-sectional areas, different air flow rates
• Objects of varying mass, same cross-sectional area, different air flow rates
• Find the terminal velocity of a falling object by dropping it through a funnel that
is inserted into the device. The funnel will serve to concentrate the air flow and
not cause the object to bounce around as it drops.
• Create an experiment where an object is “levitated” when the aerodynamic force
and the force of gravity is balanced.
2. Extend the height of the device by another meter and add another set of Infrared LED
and Infrared Detector to increase the height from which objects will be dropped.
3. Incorporate the operation of the fan into the programming. At this time, the fan is
being adjusted manually.
REFERENCES
www.lerc.nasa.gov/WWW/K-12/airplane/termv.html
www.glenbrook.k12.il.us/GBSSCI/PHYS/mmedia/netlaws/efar.html
ACKNOWLEDGMENTS
We would like to thank SUMMIT Director Dr. Vikram Kapila, SUMMIT Training
Assistants Nathan Lee, Anshuman Panda, and Padmini Vijayakumar, Teaching Assistants
Keith Ching, Billy Mark, Shing Lik Wong, and Jared Frank, and most specially our own
indefatigable teaching assistant, Daniel Remiszewski, who devoted much of his time and
expertise in helping us see our project through to completion.